The algorithm begins by first examining each vertex and adding the cheapest edge from that vertex to another in the graph, without regard to already added edges, and continues joining these groupings in a like manner until a tree spanning all vertices is completed.

Borůvka's algorithm can be shown to take O(log V) iterations of the outer loop until it terminates, and therefore to run in time O(E log V), where E is the number of edges, and V is the number of vertices in G. In planar graphs, and more generally in families of graphs closed under graph minor operations, it can be made to run in linear time, by removing all but the cheapest edge between each pair of components after each stage of the algorithm.[7]

This is our original weighted graph. The numbers near the edges indicate their weight. Initially, every vertex by itself is a component (blue circles).

{A,B,D,F}
{C,E,G}

In the first iteration of the outer loop, the minimum weight edge out of every component is added. Some edges are selected twice (AD, CE). Two components remain.

{A,B,C,D,E,F,G}

In the second and final iteration, the minimum weight edge out of each of the two remaining components is added. These happen to be the same edge. One component remains and we are done. The edge BD is not considered because both endpoints are in the same component.

A faster randomized minimum spanning tree algorithm based in part on Borůvka's algorithm due to Karger, Klein, and Tarjan runs in expected time.[9] The best known (deterministic) minimum spanning tree algorithm by Bernard Chazelle is also based in part on Borůvka's and runs in O(E α(E,V)) time, where α is the inverse of the Ackermann function.[10] These randomized and deterministic algorithms combine steps of Borůvka's algorithm, reducing the number of components that remain to be connected, with steps of a different type that reduce the number of edges between pairs of components.